I believe everyone should be proactive about their family's needs as much as they can. Watch the weather before you go. If a hurricane does happen and if you decide to ride it out at Disney, or have to ride it out, be prepared to possibly be stuck in your room for a few days (who wants to walk through 100 MPH winds to get to the Food Court to fight their way through lines?) This would mean basic needs: food (even if just snack type items, water, light (flashlight), something to do when the lights go out, etc. Don't count on being able to keep your curtains open for any natural light---I believe you are encouraged to keep the curtains drawn in the event the glass breaks. I personally feel better knowing I am prepared and don't have to rely on Disney to take care of me. Picture loooooong lines for bottled water, food, at the front desk for assistance with stuff, etc. Also--CASH----if the atm's, electronic credit card machines, etc don't work gas stations and supermarkets may not be able to process electronic transactions.
I wouldn't worry about lugging all the stuff with you. Nowadays you get enough warning before a hurricane that even if you don't have a rental car, you can take a taxi to a local grocerty store to stock up---IF they have any supplies on hand.